AQA GCSE Physics Foundation (8463), Foundation tier · Forces › Forces and motion › Describing motion along a line
Practise Distance and displacement. 7 exam-style questions on this subtopic, at up to four difficulty levels, with full mark schemes and a progress tracker. Free, no account needed.
Distance is how far an object moves; displacement is how far it ends up from its starting point in a straight line, with a direction. Expect short recall questions and calculations of distance and displacement for journeys, often with a diagram or a map.
Key facts
Distance = how far an object moves (scalar, m)
Displacement = straight-line distance from start to finish, with a direction (vector)
Displacement needs a magnitude and a direction
Distance travelled ≥ size of the displacement
Back at the start → displacement = 0
Along a line: one direction +, the other −
Notes
Distance
Distance is how far an object moves along its path.
Distance does not involve direction, so it is a scalar quantity. Its unit is the metre (m).
For a journey with several parts, add up the lengths of all the parts.
Displacement
Displacement includes both the distance an object moves, measured in a straight line from the start point to the finish point, and the direction of that straight line.
Displacement is a vector quantity. Give its magnitude and its direction, e.g. 120 m north, or 30 m on a bearing of 045°.
For motion along a straight line, choose one direction as positive: 5 m to the right is +5 m and 5 m to the left is −5 m.
Comparing distance and displacement
diagram
The distance travelled is always greater than or equal to the size of the displacement.
Distance follows the path; displacement is the straight line from start to finish.
They are equal only when the object moves in one direction along a straight line.
If an object ends where it started, e.g. after one 400 m lap of a running track, its displacement is zero but the distance travelled is 400 m.
How to answer each type of question
Explain the difference between distance and displacement
2 marksGrade 4
Distance: the length of the whole path, with no direction.
Displacement: the straight line from start to finish, with a direction.
Example. A runner completes exactly one lap of a 400 m track. State the distance travelled and the displacement of the runner. Explain your answers.
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Distance = 400 m, because distance is the length of the path followed (1). Displacement = 0 m, because the runner finishes at the start point (1).
Calculate distance and displacement along a line
3 marksGrade 5
Distance: add the lengths of all the parts.
Displacement: take one direction as positive and the other as negative, then add.
Give the displacement with a direction.
Example. A dog runs 35 m east along a beach, then 12 m west. (a) Calculate the total distance the dog travels. (b) Calculate the displacement of the dog from its starting point.
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(a) 35 + 12 = 47 m (1) (b) 35 − 12 = 23 m (1) east (1)
Don’t lose marks
Giving a displacement without a direction.
Adding the parts of an out-and-back journey to find the displacement instead of subtracting them.
Saying distance and displacement are the same thing.
In scale drawings, not saying which direction an angle is measured from.
More tips
Memory tricks
Displacement = 'as the crow flies, plus which way'.
Distance: add everything. Displacement: use + and − for opposite directions.
Right-angled journeys often use 3-4-5 triangles: 30 and 40 give 50; 0.9 and 1.2 give 1.5.
Exam technique
Use the words 'magnitude and direction' when you define displacement.
If a question uses compass directions, give your answer with a compass direction or a bearing.
Show your Pythagoras working, or write the scale you used for a scale drawing.
What each grade needs
What you need to be able to do, from the first marks up to the top grade.
Grade 3
State that distance is a scalarDistance is how far an object moves; it does not involve direction.
Grade 4
State that displacement is a vectorDisplacement is the straight-line distance from the start point to the finish point, with the direction of that line.
Grade 5
Calculate distance and displacement along a line40 m east then 15 m west: distance 55 m, displacement 25 m east.
Grade 5
Explain why displacement can be zeroAfter a round trip back to the start, the displacement is zero although the distance travelled is not.
Quick recall
Cover the answers and test yourself. The app has these as flashcards that come back just before you'd forget them.
A runner completes exactly one lap of a 400 m running track and finishes where they started. What is the distance travelled by the runner?
400 m
A robot arm moves a component 15 cm to the left, then 15 cm back to the right, returning exactly to its starting position. Calculate the total distance moved by the component.
30 cm
Is distance a scalar quantity or a vector quantity?
Scalar.
Sample questions
Written for this site in the style of AQA exam questions. They are not taken from real past papers.
Question 1Easy4 marks
A runner completes exactly one lap of a 400 m running track and finishes where they started.
(a) What is the distance travelled by the runner?[1]
(b) What is the displacement of the runner at the end of the lap?[1]
(c) Which statement describes displacement? Tick (✓) one box.[1]
The total length of the path travelled
The distance in a straight line from the start point to the finish point, and its direction
The speed of an object in a given direction
The distance travelled in one second
(d) Is displacement a scalar quantity or a vector quantity?[1]
Show the answer and mark scheme
(a)Answer: 400 m
400 (m)
(b)Answer: 0 m
0 / zero
(c)Answer: The distance in a straight line from the start point to the finish point, and its direction
(d)Answer: Vector.
vector
Question 2Medium6 marks
(a) A dog runs 25 m due east to fetch a ball, then runs 10 m due west. Calculate the total distance the dog runs.[1]
(b) Give the displacement of the dog from its starting point.[2]
(c) A hiker walks 3.0 km due north and then 4.0 km due east. Use a scale drawing to determine the magnitude of the hiker’s displacement from the starting point.[2]
(d) Use your scale drawing to determine the direction of the hiker’s displacement as a bearing (an angle measured clockwise from north).[1]
Show the answer and mark scheme
(a)Answer: 35 m
35 (m)
(b)Answer: 15 m due east m
15 (m)
(due) east
(c)Answer: 5.0 km
correct scale drawing: right-angled triangle with sides of 3.0 km (north) and 4.0 km (east) to a stated scale